THERMOELASTICITY OF A REGULARLY NONHOMOGENEOUS THIN CURVED LAYER WITH RAPIDLY VARYING THICKNESS

A regularly nonhomogeneous (composite), anisotropic, thin curved layer with rapidly oscillating material parameters and thickness is considered for the case when mean thickness and period scale have small magnitudes of the same order. A three-dimensional thermoelasticity problem for this layer is reduced to a homogenized shell model by means of an asymptotic homogenization method for periodic structures. The effective thermoelastic and thermal material parameters of this shell are expressed in terms of solutions for auxiliary local problems in the cell of periodicity. Using the solution of the boundary-value problem for the homogenized shell and the solutions of the local problems, one can obtain a three-dimensional microstructure of the stresses, displacements and temperature with a high accuracy

This general model is applied to the derivation of thermoelastic and thermal constitutive equations for network periodic shells. The relations obtained lay the foundation for a new continuous model of thermoelasticity and heat conductivity for network periodic shells and plates.